Kinetic Energy Lost in Rotational Collision

[leventa2]

Homework Statement

A bullet of mass mB = 0.0115 kg is moving with a speed of 104 m/s when it collides with a rod of mass mR = 7.93 kg and length L = 1.05 m (shown in the figure). The rod is initially at rest, in a vertical position, and pivots about an axis going through its center of mass. The bullet imbeds itself in the rod at a distance L/4 from the pivot point. As a result, the bullet-rod system starts rotating.

a) Find the angular velocity, ω, of the bullet-rod system after the collision. You can neglect the width of the rod and can treat the bullet as a point mass.

0.4304 rad/s


b) How much kinetic energy is lost in the collision?

Need to know this

Homework Equations

Ke = .5*m*v^2 Ker = .5*I*w^2

The Attempt at a Solution

.5*.0115*(104^2) - .5*((1/12)*7.93*(1.05^2)+.0115*((1.05/4)^2))(.4304^2)

5*m*v^2 - .5*I*w^2

= 62.124 J

But this answer is not correct, why?

 

[leventa2]

Moment of inertia of the rod

(1/12)*M*(h^2)

Of Bullet:

m*(r^2)